|dc.description.abstract||The penetration of magnetic fields in the form of quantized vortices in type-II superconductors is well known. However, it is not well known that such vortices can be electrically charged. The effect is quite subtle and originates from the particle-hole symmetry in a superconductor. The high Tc superconductors (HTS) are predicted to be better candidates for vortex-charge detection due to their large superconducting gap. Thus far, a direct measurement of charged cores has remained challenging due to their small value and electrostatic screening by the surrounding opposite charges.
In recent years, cavity-optomechanical techniques have emerged as an attractive method to improve the sensitivity of various measurements. Such methods have shown exquisite force sensitivities down to the standard quantum limit and control over the quantum states of the motion. Recently, such techniques have also drawn attention to probe the thermodynamic properties of atomically thin two-dimensional (2D) materials. The 2D crystals are particularly attractive for developing mechanical resonators and their integration in optomechanical device due to their low mass, and hence larger coupling with light field. Motivated from these aspects, we develop a device to directly detect the charges in the flux-vortices by measuring the electromechanical response. Here the electrostatic effect of vortex-charge is transduced to the mechanical response.
To study the vortex charge, a few UC thick crystals of high-transition temperature superconductor Bi2Sr2CaCu2O8+δ (BSCCO) is used for the mechanical resonator. One important parameter of the mechanical resonator is its resonant frequency. However, estimating the resonant frequency requires elastic modulus like Young's modulus and pre-tension in the flake. While the elastic coefficients of the bulk crystals of BSCCO have been observed with large variations, there is no investigation into the elastic properties of a few UC thick nanoscale samples. Further, the mechanical properties of a few unit cells (UC) thick exfoliated crystals could be significantly different from their bulk counterpart.
To begin with, we present systematic measurements of the mechanical properties of a few unit cells (UC) thick exfoliated crystals of a high-Tc cuprate superconductor BSCCO. We determine the elastic properties of these crystals by deformation using an atomic force microscope (AFM) at room temperature. With the spatial measurements of local compliance and their detailed modelling, we determine Young's modulus of rigidity and the pre-stress. Young's modulus of rigidity is found to be in the range of 22 GPa to 30 GPa for flakes with thickness from 5 UC to 18 UC. The pre-stress spreads over the range of 5 MPa - 46 MPa, indicating a run-to-run variation during the exfoliation process. The determination of Young's modulus of rigidity for thin flakes is further verified from the recently reported buckling technique .
In the next chapter, we present nanoelectromechanical resonators fabricated with thin exfoliated crystals of BSCCO. The mechanical r= eadout is performed by capacitively coupling their motion to a coplanar waveguide microwave cavity fabricated with a superconducting alloy of molybdenum-rhenium (MoRe). We demonstrate mechanical frequency tunability with external dc-bias voltage and quality factors up to ~36600. Our spectroscopic and time-domain measurements show that mechanical dissipation in these systems is limited by the contact resistance arising from resistive outer layers. The temperature dependence of dissipation indicates the presence of tunnelling states, further suggesting that their intrinsic performance could be as good as other two-dimensional atomic crystals such as grap= hene .
Learning from these two experiments, we improve the performance of the device and carry out the mechanical exfoliation in inert atmosphere. We integrate a mechanical resonator made of a thin flake of HTS BSCCO into a microwave circuit to realize a cavity-electromechanical device. In the final chapter, we studied the electromechanical response of the mechanical resonator when a magnetic field perpendicular to the CuO2 plane is applied. As the magnetic field penetrates the surface of a superconductor, it results in the formation of flux-vortices. These flux-vortices will have charged vortex core and create a dipolelike electric field. Due to the exquisite sensitivity of cavity-based devices to the external forces, we directly detect the charges in the flux vortices by measuring the electromechanical response of the mechanical resonator . Our measurements reveal the strength of surface electric dipole moment due to a single vortex core to be approximately 30 |e|aB, where aB is the Bohr radius and e is the electron charge. Further, using the value of surface dipole moment, we have estimated the vortex line charge to be +4.9 × 10-2|e|/nm, which is equivalent to a charge per CuO_2 layer to be +3.7 × 10-2|e|.||en_US